Math and the Real World

Three years ago I didn’t even know I liked math and had never programmed; now I’m an applied math major considering a career in statistics.

I spent last summer exploring the ways in which math can be used to solve real-life problems. At a six-week research experience for undergraduates (REU) hosted by Macalester and the Institute for Mathematics and its Applications, I worked with students from colleges across the country on a real-world question:

By looking at video or pictures of, for example, metal with a dent in it, can we identify the location of the dent without any prior information about it?

This problem was posed by a University of Minnesota electrical engineering professor who hopes to find ways to identify structural defects (again, think dents in metal).

Because the REU was interdisciplinary, it helped that Mac’s MSCS Department includes math and computer science classes as well as applied math. I was thrilled to find that topics covered in my Macalester classes were useful for this research. Alicia Johnson, a professor in Macalester’s Mathematics, Statistics, and Computer Science Department, was our advisor.

We wanted to see if “dictionary learning techniques” could be applied to anomaly detection problems. Dictionary learning methods are used to find the best way to represent information by less, while making sure that the representation is still a good representation of the data.

My main goal was to see how applied math research is done—and through this REU, I was able to do just that. In January my research group is presenting its work at the Joint Mathematics Meetings in Baltimore. This will bring the process full circle because presenting results and ideas is the important next step after working on a problem.